Bayesian Model Selection for Longitudinal Count Data

Oludare Ariyo (), Emmanuel Lesaffre, Geert Verbeke and Adrian Quintero
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Oludare Ariyo: Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat)
Emmanuel Lesaffre: Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat)
Geert Verbeke: Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat)
Adrian Quintero: Icfes - Colombian Institute for Educational Evaluation

Sankhya B: The Indian Journal of Statistics, 2022, vol. 84, issue 2, No 4, 516-547

Abstract: Abstract We explore the performance of three popular model-selection criteria for generalised linear mixed-effects models (GLMMs) for longitudinal count data (LCD). We focus on evaluating the conditional criteria (given the random effects) versus the marginal criteria (averaging over the random effects) in selecting the appropriate data-generating model. We advocate the use of marginal criteria, since Bayesian statisticians often use the conditional criteria despite previous warnings. We discuss how to compute the marginal criteria for LCD by a replication method and importance sampling algorithm. Besides, we show via simulations to what extent we err when using the conditional criteria instead of the marginal criteria. To promote the usage of the marginal criteria, we developed an R function that computes the marginal criteria for longitudinal models based on samples from the posterior distribution. Finally, we illustrate the advantages of the marginal criteria on a well-known data set of patients who have epilepsy.

Keywords: Replication sampling; Marginal likelihood; Bayesian model selection.; Primary 62C10; Secondary 62P10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13571-021-00268-9

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